An Internal Derivation of the Fine-Structure Constant

This paper presents a computational structure that internally derives the fine-structure constant \(\alpha\) as the low-energy normalized prefactor of the \(V_{p2.2}\)-EM electromagnetic channel, rather than taking it as an exogenous empirical constant.The starting point is the \(V_{p1.0}\) common event-extraction engine and the \(V_{p2.2}\)-EM channel compilation. First, the coupling-free bare electromagnetic tensor \(\widetilde T_{\mu\nu}^{(\mathrm{EM})}\) is separated from the physical electromagnetic ledger, and the position into which \(\alpha^{-1}/4\pi\) enters is sealed in advance as\[T_{\mu\nu}^{(2),\mathrm{phys}}=\frac{\alpha^{-1}(t,\Omega_\alpha)}{4\pi}\widetilde T_{\mu\nu}^{(\mathrm{EM})}+\Delta_{\mu\nu}^{(2)}+J_{\mu\nu}^{(2,\mathrm{src})}.\]On this position fixing, the electromagnetic trace-like \(U(1)\) projection-capacity certificate is produced from internal projection impedance as\[C_\Pi^{(\alpha,0)}=0.3817992348991862\ldots .\]Substituting this into the zeroth-order capsule-average loss gives the leading normalization mode\[\alpha^{-1}_{(0)}=136.9503259827925\ldots .\]Next, on the edge-trigger plateau branch selected by the time engine and the ternary implementation residual, the bounded trigger correction\[\delta_{\mathrm{trig}}^{(\alpha,0)}=0.0856731937361413\ldots\]is internally produced.Therefore, the final internal electromagnetic normalization coefficient is\[\alpha^{-1}_{\mathrm{int}}=\alpha^{-1}_{(0)}+\delta_{\mathrm{trig}}^{(\alpha,0)}=137.0359991765286\ldots .\] This paper interprets this value not as an arbitrary \(q^2\neq0\) running coupling, but as the reference value of the low-energy on-shell or Thomson-limit electromagnetic normalization branch,\[\alpha^{-1}_{\mathrm{int}}\equiv\alpha_{\mathrm{OS}}^{-1}(0;\Omega_\alpha).\]Running at \(q^2\neq0\) is separated into vacuum-polarization and higher-resolution readout-correction branches. The same zeroth-order base ledger also produces, without using \(C_\Pi^{(\alpha,0)}\) or \(\delta_{\mathrm{trig}}^{(\alpha,0)}\), the independent scale-separation readout\[R_\Omega/\ell_\Omega=1074.03933765\ldots .\]When anchored by the electron reduced Compton scale \(R_{\Omega_\alpha} = \bar{\lambda}_C = \hbar/(m_e c)\), this independent readout defines\(\ell_{\Omega_\alpha}=0.3595392216\,\mathrm{fm}\)as the electromagnetic implementation cell and minimal readout scale, namely an object-local minimal implementation cell. The claim of this paper is not that a particular number is fitted after the fact. The computational order is fixed as follows: the position of \(\alpha\), bare/normalized separation, internal derivation of \(C_\Pi^{(\alpha,0)}\), bounded production of \(\delta_{\mathrm{trig}}^{(\alpha,0)}\), low-energy QED scheme identification, independent readout, and consistency check against an external reference anchor. The later-stage readout-boundary, time-engine, support-layer, and master-action structures are presented in compressed form in the appendices to the extent required.